Titlebook: Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties; Yukiyoshi Nakkajima,Atsushi Shiho Book 2008 Sprin

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Weight Filtrations on Log Crystalline Cohomologies,y and the .-degeneration of .-adic weight spectral sequences. We also prove that our weight filtration on log crystalline cohomology coincides with the one defined by Mokrane in the case where the base scheme is the spectrum of a perfect field of characteristic . < 0.

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Preliminaries on Filtered Derived Categories and Topoi, because our weight-filtered complexes will be defined as objects in certain filtered derived categories. In the last two sections, we recall the notion of topoi associated to diagrams of topoi and prove several basic properties of the topoi associated to diagrams of (restricted) log crystalline topoi.

艰苦地移动

Weight Filtrations on Log Crystalline Cohomologies,y and the .-degeneration of .-adic weight spectral sequences. We also prove that our weight filtration on log crystalline cohomology coincides with the one defined by Mokrane in the case where the base scheme is the spectrum of a perfect field of characteristic . < 0.

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Book 2008Poincaré duality, and the E.2.-degeneration of p-adic weight spectral sequences. In addition, the authors state some theorems on the weight filtration and the slope filtration on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0..

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Preliminaries on Filtered Derived Categories and Topoi,s, we recall several notions and basic properties concerning filtered derived categories: filtered complex, filtered quasi-isomorphism, filtered derived category, filtered injective resolution, filtered flat resolution, filtered derived functor and filtered adjunction formula. It is important for us

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Weight Filtrations and Slope Filtrations on Rigid Cohomologies (Summary),f a separated scheme of finite type over a perfect field of characteristic . < 0. They are constructed and calculated by using de Jong’s alteration theorem, Tsuzuki’s proper cohomological descent for rigid cohomology, the comparison theorem between log crystalline cohomology and rigid cohomology by